AQA GCSE Half Life

AQA GCSE Half Life

Half Life

There are two possible definitions, either is suitable:

The half-life of a radioactive isotope is the time it takes for the number of nuclei of the isotope in a sample to halve. 

The time it takes for the count rate (or activity) from a sample containing the isotope to fall to half its initial level.

The one you would choose, depends on the situation. If the the data is showing the number of nuclei decreasing, then use the first one. If the data shows the count rate decreasing, then the 2nd one would be used. 

Half life graphs

Graph for radioactive decay showing becquerels decreasing over time

At the start the first activity reading is 10 x 106 Bq.

To find the half life, we will halve this value which is 5 x 106 Bq. Then draw a horizontal line from axis at 5 x 106 Bq to graph line. Finally, continue to draw the line, but downwards toward the time axis.

Radioactive decay graph to show the half life of 4 minutes

The line is shown in red, the half life for this isotope is 4 minutes. 

Sometimes, you need to show constant half life on a graph, so the process needs to be repeated. As shown in the graph below.

Graph to show 2 half lives for radioactive decay, to prove constant half life

The graph above shows two half lives. Each half life is 4 minutes.

1st half life starts at 0 minutes and ends at 4 minutes.

2nd half life starts at 4 minutes and ends at 8 minutes. 

This shows us that each isotope has a constant half life. 

This means that for this isotope, every 4 mintes the count rate will halve. 

Tip: In the exam, draw the lines onto the graph with a ruler, there is often a mark for this!

Practice Questions

1.Using the graph below estimate the half life for the sample. 

Half life sample question

2. Using the graph below estimate the half life for the sample

Calculate the half life of a radioactive substance from a graph

3. Use the data in the table below to plot your own graph and calculate the half life. 

Time (seconds)Activity (counts per second)
0241
30212
60188
90165
120145
150127
180112
21099
24087
27076
30067
33059
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